It's not a ridiculous thought. It's actually pretty common. The rules vary slightly state to state and usually require filing returns in two states; but double taxation is rare.
In your case there is no effect at all. You will continue to pay AL income tax on all your income, including the TN wages. Since TN does not have an income tax, you won't have to deal with TN. The bottom line is that working in TN does not get you out of paying AL tax.
